Topologies, Migration Rates, and Multi-Population Parallel Genetic Algorithms

This paper presents a study of parallel genetic algorithms (GAs) with multiple populations (also called demes or islands). The study makes explicit the relation between the probability of reaching a desired solution with the deme size, the migration rate, and the degree of the connectivity graph. The paper considers arbitrary topologies with a fixed number of neighbors per deme. The demes evolve in isolation until each converges to a unique solution. Then, the demes exchange an arbitrary number of individuals and restart their execution. An accurate deme-sizing equation is derived, and it is used to determine the optimal configuration of an arbitrary number of demes that minimizes the execution time of the parallel GA.

[1]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[2]  Paul Bryant Grosso,et al.  Computer Simulations of Genetic Adaptation: Parallel Subcomponent Interaction in a Multilocus Model , 1985 .

[3]  D. Goldberg,et al.  Predicting Speedups of Idealized Bounding Cases of Parallel Genetic Algorithms , 1997 .

[4]  Erick Cantú-Paz,et al.  Modeling Idealized Bounding Cases of Parallel Genetic Algorithms , 1996 .

[5]  Kalyanmoy Deb,et al.  Genetic Algorithms, Noise, and the Sizing of Populations , 1992, Complex Syst..

[6]  David E. Goldberg,et al.  Predicting Speedups of Ideal Bounding Cases of Parallel Genetic Algorithms , 1997, ICGA.

[7]  Hans-Georg Beyer,et al.  Toward a Theory of Evolution Strategies: Some Asymptotical Results from the (1,+ )-Theory , 1993, Evolutionary Computation.

[8]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.

[9]  S. Finch.  Gambler's Ruin , 2022 .

[10]  C. R. Henson.  Conclusion , 1969 .

[11]  David E. Goldberg,et al.  Efficient Parallel Genetic Algorithms: Theory and Practice , 2000 .

[12]  H. Leon Harter,et al.  Order statistics and their use in testing and estimation , 1970 .

[13]  Masaharu Munetomo,et al.  An Efficient Migration Scheme for Subpopulation-Based Asynchronously Parallel Genetic Algorithms , 1993, ICGA.

[14]  E. Cantu-Paz,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1997, Evolutionary Computation.

[15]  David E. Goldberg,et al.  Two analysis tools to describe the operation of classifier systems , 1989 .

[16]  Heinrich Braun,et al.  On Solving Travelling Salesman Problems by Genetic Algorithms , 1990, PPSN.